论文标题
不断发展的表面上非线性Cahn-Hilliard型方程的稳定性和误差估计值
Stability and error estimates for non-linear Cahn-Hilliard-type equations on evolving surfaces
论文作者
论文摘要
在本文中，我们考虑了具有规定速度的不断发展的表面上Cahn-Hilliard型的非线性四阶演化方程，其中仅假定非线性术语具有局部Lipschitz衍生物。高阶不断发展的表面有限元元素用于离散空间中的弱方程系统，并得出了半混凝土问题的修改矩阵矢量公式。方程系统的抗对称结构通过空间离散保留。基于此结构的新稳定性证明与一致性边界相结合，证明了最佳订购和均匀的误差估计。该论文以多种数值实验结束。
In this paper, we consider a non-linear fourth-order evolution equation of Cahn-Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order evolving surface finite elements are used to discretise the weak equation system in space, and a modified matrix-vector formulation for the semi-discrete problem is derived. The anti-symmetric structure of the equation system is preserved by the spatial discretisation. A new stability proof, based on this structure, combined with consistency bounds proves optimal-order and uniform-in-time error estimates. The paper is concluded by a variety of numerical experiments.
